A within-day dynamic traffic assignment model for urban road networks

In this paper a new formulation of within-day dynamic traffic assignment is presented, where a dynamic user equilibrium is expressed as a fixed-point problem in terms of arc flow temporal profiles. Specifically, it is shown that, by extending to the dynamic case the concept of network loading map, one need not introduce the continuous network loading problem in order to ensure the temporal consistency of the supply model. On this basis it is possible to devise efficient assignment algorithms, based on piece-wise linear or piece-wise constant approximation of temporal profiles over predefined time intervals covering the period of analysis, whose complexity is equal to the one resulting in the static case multiplied by the number of time intervals. With specific reference to a Logit path choice model, an implicit path enumeration network loading procedure is obtained as an extension of Dial's algorithm; then, the fixed-point problem is solved through the Bather's method.